Integrable Systems and Mathematical Physics Seminar, University of
Glasgow, September 22, 2026
John Baez
Second Quantization for the Kepler Problem
The Kepler problem concerns a point particle in an attractive inverse
square force. After a brief review of the classical and quantum
versions of this problem, focused on their hidden symmetries, we turn
to the quantum Kepler problem for a spin-½ particle. We
show that the Hilbert space \(\mathcal{H}\) of bound states for this
problem is unitarily equivalent to the Hilbert space of solutions of a
massless chiral spin-½ particle on the spacetime
\(\mathbb{R} \times S^3\). The fermionic Fock space on
\(\mathcal{H}\) is thus equivalent to the Hilbert space of a massless
chiral spin-½ free quantum field on \(\mathbb{R} \times
S^3\). By modifying the Hamiltonian on this Fock space, we obtain one
that gives the well-known "Madelung rules", which describe the rough
overall structure of the periodic table.
You can see my slides here and read
the paper my talk is based on:
© 2026 John Baez
baez@math.removethis.ucr.andthis.edu
